An example of such a deburring tool is disclosed in U.S. Pat., No. 5,755,538 in accordance with which a cutting insert with a cutting portion, loaded by a spring engaged in a rear groove of the insert, is held in a radially, outwardly sealed window in a tool holder. In the first embodiment, the insert is guided slidable in the tool holder and can, accordingly, be moved in or out by a radial sliding or swinging out of the window of the tool holder. The insert is designed with a lateral groove which is located perpendicular to its longitudinal axis. In the area of this groove, a tension pin is engaged perpendicular to the cutting portion-longitudinal axis and flush in the tool holder and is fixed by the size of the groove in the insert-sliding direction of the insert-sliding path in the window-sliding direction. The insert has only one cutting portion comprising two cutting edges. One cutting edge being operative in the forward direction and the other in the reverse direction.